On a class of new hypergeometric transformations

In this article we continue the investigations presented in our previous papers [1,2,3,4], presenting some, for the best of our knowledge, new transformations of the Gauss hypergeometric function (3) and (13). They have been obtained using only elementary methods and stem from a couple of integrals...

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Main Authors:	Giovanni Mingari Scarpello, Daniele Ritelli
Format:	Article
Language:	English
Published:	Ptolemy Scientific Research Press 2018-04-01
Series:	Open Journal of Mathematical Sciences
Subjects:	Hypergeometric function; Complete elliptic integral; Hypergeometric transformations; Modular transformations.
Online Access:	https://openmathscience.com/on-a-class-of-new-hypergeometric-transformations-2/

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spelling	doaj-4050a50380854ebcb0e3827f73d1a8112020-11-25T01:36:59ZengPtolemy Scientific Research PressOpen Journal of Mathematical Sciences2616-49062523-02122018-04-01219311410.30538/oms2018.0019On a class of new hypergeometric transformationsGiovanni Mingari Scarpello0Daniele Ritelli1via Negroli, 6 Milan, Italy.Dipartimento di Scienze Statistiche, via Belle Arti, 41, 40126 Bologna Italy.In this article we continue the investigations presented in our previous papers [1,2,3,4], presenting some, for the best of our knowledge, new transformations of the Gauss hypergeometric function (3) and (13). They have been obtained using only elementary methods and stem from a couple of integrals evaluated in terms of complete elliptic integral of first kind by Legendre in [5] Chapter XXVII, at sections II and III.https://openmathscience.com/on-a-class-of-new-hypergeometric-transformations-2/Hypergeometric function; Complete elliptic integral; Hypergeometric transformations; Modular transformations.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Giovanni Mingari Scarpello Daniele Ritelli
spellingShingle	Giovanni Mingari Scarpello Daniele Ritelli On a class of new hypergeometric transformations Open Journal of Mathematical Sciences Hypergeometric function; Complete elliptic integral; Hypergeometric transformations; Modular transformations.
author_facet	Giovanni Mingari Scarpello Daniele Ritelli
author_sort	Giovanni Mingari Scarpello
title	On a class of new hypergeometric transformations
title_short	On a class of new hypergeometric transformations
title_full	On a class of new hypergeometric transformations
title_fullStr	On a class of new hypergeometric transformations
title_full_unstemmed	On a class of new hypergeometric transformations
title_sort	on a class of new hypergeometric transformations
publisher	Ptolemy Scientific Research Press
series	Open Journal of Mathematical Sciences
issn	2616-4906 2523-0212
publishDate	2018-04-01
description	In this article we continue the investigations presented in our previous papers [1,2,3,4], presenting some, for the best of our knowledge, new transformations of the Gauss hypergeometric function (3) and (13). They have been obtained using only elementary methods and stem from a couple of integrals evaluated in terms of complete elliptic integral of first kind by Legendre in [5] Chapter XXVII, at sections II and III.
topic	Hypergeometric function; Complete elliptic integral; Hypergeometric transformations; Modular transformations.
url	https://openmathscience.com/on-a-class-of-new-hypergeometric-transformations-2/
work_keys_str_mv	AT giovannimingariscarpello onaclassofnewhypergeometrictransformations AT danieleritelli onaclassofnewhypergeometrictransformations
_version_	1725060447384633344

On a class of new hypergeometric transformations

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